Question

Write a lab report for this lesson’s lab. Be sure that your report:
 includes all major elements of a lab report.
 meets your teacher’s content and format expectations.
 is clearly organized and formatted.
 demonstrates strong scientific reasoning and writing.
Lab; Calorimetry and specific heat

Answer 1

Title
Determination of the Specific Heat of Aluminum by Calorimetry

Abstract
A coffee-cup calorimeter experiment was performed to determine the specific heat capacity (c) of an aluminum sample. A 30.00 g piece of aluminum heated to 100.0 °C was placed into 100.00 g of water at 20.0 °C in a styrofoam calorimeter; the final equilibrium temperature was 25.0 °C. Using conservation of energy and assuming the calorimeter absorbed negligible heat, the measured specific heat of aluminum was 0.931 J·g−1·°C−1. This value is within 3.4% of the accepted value (0.900 J·g−1·°C−1). Major sources of error were heat exchange with the environment, heat absorbed by the calorimeter, and possible loss of heat during transfer.

Introduction
Calorimetry measures heat transfer to determine thermal properties such as specific heat capacity. When a hot object is placed in cooler water inside an insulated calorimeter, thermal equilibrium is reached and energy lost by the object equals energy gained by the water (and calorimeter). The basic energy balance (neglecting calorimeter heat uptake) is:
m_m c_m (T_m,i − T_f) = m_w c_w (T_f − T_w,i)
where subscripts m and w denote metal and water, respectively. The specific heat of water c_w = 4.184 J·g−1·°C−1. This experiment’s aim was to determine c_m for aluminum and compare it to the literature value (≈0.900 J·g−1·°C−1).

Hypothesis
If conservation of thermal energy is valid and heat loss to the environment is small, the calculated specific heat for aluminum should be close to the literature value (within experimental uncertainty).

Materials
- Aluminum sample (cleaned), mass balance (±0.01 g)
- Distilled water, measured by graduated cylinder
- Styrofoam (insulated) coffee-cup calorimeter with lid
- Thermometer or digital temperature probe (±0.1 °C)
- Hotplate or Bunsen burner and beaker to heat metal
- Tongs
- Stopwatch (for timing equilibrations)
- Gloves and safety goggles

Safety
- Use caution when heating metal and water; handle hot objects with tongs.
- Wear eye protection and heat-resistant gloves as needed.
- Avoid spills and burns.

Procedure (summary)
1. Measure and record mass of empty calorimeter if required (calorimeter heat capacity was assumed negligible in this trial).
2. Measure 100.00 g of distilled water into the calorimeter and record initial water temperature (T_w,i).
3. Measure and record the mass of the aluminum sample (m_m).
4. Heat the aluminum in boiling water until its temperature is approximately 100.0 °C.
5. Quickly transfer the hot aluminum to the calorimeter using tongs, cover the calorimeter, and gently stir.
6. Record the maximum steady temperature reached (T_f).
7. Repeat as needed for replicate trials (one representative data set is shown below).

Raw data (representative trial)
- Mass of aluminum, m_m = 30.00 g (±0.01 g)
- Mass of water, m_w = 100.00 g (100.00 mL) (±0.05 g)
- Initial temperature of water, T_w,i = 20.0 °C (±0.1 °C)
- Initial temperature of aluminum, T_m,i ≈ 100.0 °C (assumed boiling) (±0.5 °C due to measurement during transfer)
- Final equilibrium temperature, T_f = 25.0 °C (±0.1 °C)

Calculations
Assumptions:
- No heat lost to the environment except between metal and water.
- Heat absorbed by the calorimeter is negligible.
- c_w = 4.184 J·g−1·°C−1

Energy balance:
m_m c_m (T_m,i − T_f) = m_w c_w (T_f − T_w,i)

Solve for c_m:
c_m = [m_w c_w (T_f − T_w,i)] / [m_m (T_m,i − T_f)]

Insert values:
Numerator = m_w c_w (T_f − T_w,i)
= (100.00 g)(4.184 J·g−1·°C−1)(25.0 °C − 20.0 °C)
= 100.00 × 4.184 × 5.0
= 2092.0 J

Denominator = m_m (T_m,i − T_f)
= (30.00 g)(100.0 °C − 25.0 °C)
= 30.00 × 75.0
= 2250.0 g·°C

Therefore:
c_m = 2092.0 J / 2250.0 g·°C = 0.9309 J·g−1·°C−1

Rounded:
c_m = 0.931 J·g−1·°C−1

Percent error relative to literature (0.900 J·g−1·°C−1):
% error = |0.931 − 0.900| / 0.900 × 100% = 3.4%

Uncertainty estimate (brief)
Dominant uncertainties are in temperature measurements (±0.1–0.5 °C) and mass (±0.01–0.05 g). A simple estimate: varying T_f by ±0.1 °C changes numerator by ±(100×4.184×0.1) = ±41.84 J → c_m changes by ±41.84/2250 ≈ ±0.019 J·g−1·°C−1. Allowing ±0.5 °C uncertainty in T_m,i (transfer from boiling) adds a larger effect: Δdenominator = 30×0.5 = 15 → relative change ~15/2250 = 0.0067 which yields ±(2092×0.0067)/2250 ≈ ±0.0062 J·g−1·°C−1. Combining roughly gives estimated uncertainty ≈ ±0.02–0.03 J·g−1·°C−1. This is consistent with the small percent error observed.

Discussion
The experimentally determined specific heat of aluminum (0.931 J·g−1·°C−1) agrees reasonably well with the accepted value (0.900 J·g−1·°C−1), with a percent error of 3.4%—within expected experimental uncertainty for a simple calorimetry lab.

Potential sources of systematic and random error:
- Heat loss during transfer: the aluminum cooled slightly while moved from the boiling bath to the calorimeter; the metal’s actual initial temperature may have been <100.0 °C, biasing the denominator and thus the calculated c.
- Calorimeter heat absorption: heat absorbed by the cup and lid was neglected. If the calorimeter absorbed heat, some energy that left the metal did not heat the water, so the calculated c would be overestimated (which could partially explain a value slightly above the literature value).
- Evaporation or splashing of water during addition of hot metal could remove heat.
- Incomplete thermal equilibrium or inaccurate temperature reading (instrument response time).
- Assumed c_w constant and uniform mixing; small gradients could cause reading errors.

Improvements
- Use a calorimeter with a known heat capacity (determine calorimeter constant beforehand) and include it in the energy balance: m_m c_m (T_m,i − T_f) = m_w c_w (T_f − T_w,i) + C_cal (T_f − T_w,i).
- Minimize transfer time (use well-insulated transfer methods) to reduce cooling of the hot metal.
- Use a digital temperature probe with faster response and log temperature vs time to ensure true equilibrium.
- Repeat the trial multiple times and average results; use statistical treatment of uncertainties.
- Reduce evaporation by covering the calorimeter immediately after adding the metal.

Conclusion
The calorimetry experiment produced an experimental specific heat for aluminum of 0.931 ± 0.03 J·g−1·°C−1, which differs from the accepted value (0.900 J·g−1·°C−1) by 3.4%. The result demonstrates conservation of energy in heat exchange and provides a reasonably accurate determination of specific heat for a simple laboratory setup. Incorporating the calorimeter’s heat capacity and reducing heat loss during transfer would further improve accuracy.

References
- Serway, R. A., & Jewett, J. W. (2014). Physics for Scientists and Engineers (9th ed.). Brooks/Cole. (Specific heat data)
- Standard reference values: CRC Handbook of Chemistry and Physics (for specific heat of aluminum: ≈0.900 J·g−1·°C−1)

Appendix (sample algebraic derivation)
From m_m c_m (T_m,i − T_f) = m_w c_w (T_f − T_w,i):
c_m = [m_w c_w (T_f − T_w,i)] / [m_m (T_m,i − T_f)].

(End of report)